In a 30° - 60° - 90° triangle, the longer leg is which of the following?
(Points : 1)

a) 3 times the length of the shorter leg

b) 2 times the length of the hypotenuse

c) 2 times the length of the shorter leg

d) 3 times the length of the hypotenuse

Question

In a 30° - 60° - 90° triangle, the longer leg is which of the following?
(Points : 1)

a) 3 times the length of the shorter leg

b) 2 times the length of the hypotenuse

c) 2 times the length of the shorter leg

d) 3 times the length of the hypotenuse

anonymous · Answer

A 30o - 60o - 90o triangle is formed by splitting an equilateral triangle in two. 

 If the equilateral triangle has side lengths of 2, that means the bottom triangle leg now was a length of 1, with a hypoteneuse of 2. 

 By using the Pythagorean theorem, we find that the remaining side is root 2. 

 Thus, the answer is root 3 times the length of the shorter leg.

anonymous · Answer

does that help? @allibricker12

anonymous · Answer

thank you so much! @kittenlover731

anonymous · Answer

what about this? @kittenlover731 

In a 30° - 60° - 90° right triangle, the hypotenuse has a length of 8. What is the length of the longer leg?

a) 4

b) 8

c) 4$$\sqrt{3}$$

d) 4$$\sqrt{2}$$

anonymous · Answer

The length of the two legs are, shorter leg = 8*sin30 and longer leg = 8sin60 
 sin60 = √3/2 

 Longer leg = 8√3/2 = 4√3

anonymous · Answer

sorry that took so long :/

anonymous · Answer

it's okay! one more I promise! 
In a 45° - 45° - 90° triangle, the length of the hypotenuse is which of the following?

a) 3 times the length of one leg

b) 2 times the length of one leg

c)  ½ times the length of one leg

d) 1 times the length of one leg

anonymous · Answer

@kittenlover731

anonymous · Answer

There are two angles of 45 which means that the triangle is isosceles. We can mark the two legs as x. 
 We also know that according to the Pythagorean theorem, in this right triangle x² + x² = hypotenuse². 

SO... 
 hypotenuse = √2x² = √2√x² = x√2 = sqrt of 2 times the length on one leg

anonymous · Answer

so b?

anonymous · Answer

yep :D

anonymous · Answer

Anything else?

anonymous · Answer

thank you so much! Well I have a question but I don't want to bother you.

anonymous · Answer

well I would try to answer it but I have a d in language arts and I have to get to work so :/

anonymous · Answer

well i'll put it in if you can answer it. & let me know if it will take to long. 

Find the value of x.

 a) 4

 b) 6

 c) 10

 d) 16

anonymous · Answer

& ew english. I hate english. I hope there is someone here that can help you with that!

anonymous · Answer

im sorry but I really need to get to work so I cant help :( sorry @allibricker12